Algebra II
posted by Matt on .
can you help answer this question please; four algebra formulas for Amadeus traveled 760 miles in twice the time it took his nemesis Salieri to travel 220 miles. if Amadeus"s rate exceeded Salieri's by 40 miles per hour, what were the rate and time for each man?

Two equations:
1.) Amadeus
760miles=R1*T1
2.) Salieri
220miles=R2*T2
Let R1=R2+40
and
Let T1=2*T2
Substitute into equations and solve:
760miles=(R2+40)*(2*T2)
Solving for T2:
380 miles/(R2+40)=T2
Plug into equation 2 and solve for R2:
220 miles=R2*[380 miles/(R2+40)]
220 miles*R2+8,800 miles=R2*380 miles
160 miles*R2=8,800 miles
R2=55 miles/hr
Solve for other variables using the two equations or the T and R equations:
=================================
R1=R2+40=55+40=95 miles/hr
T2=220 miles/R2=R=220 miles/55=4 Hr
T1=2*T2=2*(4)=8 Hr
R2=55 miles/hr